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Self-gravitating quantum stars with a globally relevant Bohm potential

Ilídio Lopes

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Phys. Rev. D 113, 115043 – Published 16 June, 2026

DOI: https://doi.org/10.1103/m6jf-8cyl

Abstract

The microphysics underlying nonbaryonic dark matter remains unknown. I derive the two-species Schrödinger-Poisson-Yukawa system for spin-12 dark-sector fermion fields, ψ (mass m1) and χ (mass m2), coupled through a scalar mediator of mass mϕ via a universal Yukawa coupling, within an orbital-free density-functional framework with the Kirzhnits gradient coefficient λB=1/9. A central result is that the Bohm potential, far from being negligible in the Thomas-Fermi regime, contributes a species-dependent surface-energy correction analogous to the nuclear liquid-drop model; the heavier fermion species generates an outward quantum-pressure wall whilst the lighter species provides an inward surface tension, with degeneracy pressure furnishing the bulk confinement. In the single-species Schrödinger-Poisson limit the ground state recovers the benchmarked invariants Mdim≃3.883 and xT≃2.562, yielding MRT≃9.95λBℏ2/(Gm12). For polytropic index γ=5/3 the mass-radius relation satisfies R∝M−1/3; for γ=4/3 a limiting mass emerges above which no stable equilibrium exists. Illustrative configurations span M=10−8–5M⊙, m1∼10−14−10−6  eV, and radii from a few km to ∼103R⊙, with gravitational-wave contact frequencies in the Einstein Telescope and LISA bands and microlensing signatures accessible to current surveys. The predictive rigidity of the resulting mass-radius relation, in which the single microphysical parameter m1 determines the equilibrium radius once the total mass is specified, furnishes a reproducible, first-principles reference for constraining the dark-fermion mass in multicomponent dark sectors.

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Phys. Rev. D 113, 115043– Published 16 June, 2026
  • Received 23 March 2026
  • Accepted 19 May 2026
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